NOTE Need to examine all MIs for strict model and drop items accordingly.
As part of this process, outputting the alpha coefficients.
## **Wave 1**
## aspfin bfa_mt bfas_ac bfas_ap bfas_ci bfas_co bfas_ea
## alpha 0.8007216 0.7922283 0.88408 0.7814323 0.8559713 0.7748649 0.8882828
## bfas_ee bfas_nv bfas_nv9 bfas_nw bfas_oi bfas_oo
## alpha 0.8547331 0.9113937 0.9010348 0.8781388 0.8287349 0.7899743
## bfi_a bfi_a6 bfi_c bfi_d_scale bfi_e bfi_hp8
## alpha 0.8009146 0.7908462 0.819993 0.7966031 0.8749101 0.6762593
## bfi_n bfi_o bfi_s_scale hrz_col hrz_ind usi
## alpha 0.8582059 0.7898225 0.7969331 0.7126198 0.550577 0.6732525
## vrt_col vrt_ind
## alpha 0.6743606 0.6523363
## mvi
## alpha 0.6078291
## **Wave 2**
## aspfin bfa_mt bfas_ac bfas_ap bfas_ci bfas_co
## alpha 0.8252445 0.7796828 0.8829338 0.7785236 0.8492025 0.7839002
## bfas_ea bfas_ee bfas_nv bfas_nv9 bfas_nw bfas_oi
## alpha 0.8761572 0.8590842 0.8972032 0.8854566 0.8698163 0.8153715
## bfas_oo bfi_a bfi_a6 bfi_c bfi_d_scale bfi_e
## alpha 0.7970451 0.7962796 0.7961057 0.8071378 0.7858279 0.8664445
## bfi_hp8 bfi_n bfi_o bfi_s_scale hrz_col hrz_ind
## alpha 0.6848438 0.8587661 0.7966047 0.7848152 0.6932522 0.5938064
## usi vrt_col vrt_ind
## alpha 0.6929115 0.7115297 0.6393136
## mvi
## alpha 0.6322902
## **Wave 3**
## aspfin bfa_mt bfas_ac bfas_ap bfas_ci bfas_co
## alpha 0.8338066 0.8026428 0.8862414 0.7768773 0.8492295 0.7774236
## bfas_ea bfas_ee bfas_nv bfas_nv9 bfas_nw bfas_oi
## alpha 0.8819575 0.8616749 0.9007862 0.8903142 0.8817477 0.8376555
## bfas_oo bfi_a bfi_a6 bfi_c bfi_d_scale bfi_e
## alpha 0.8028977 0.803164 0.7982502 0.8213291 0.7909743 0.8728148
## bfi_hp8 bfi_n bfi_o bfi_s_scale hrz_col hrz_ind
## alpha 0.6738761 0.8582405 0.8133423 0.7918976 0.7079314 0.5391312
## usi vrt_col vrt_ind
## alpha 0.6881401 0.6990938 0.6752587
## mvi
## alpha 0.6560747
## **Wave 4**
## aspfin bfa_mt bfas_ac bfas_ap bfas_ci bfas_co bfas_ea
## alpha 0.8347909 0.7945824 0.8874039 0.7633623 0.8518579 0.7937478 0.881371
## bfas_ee bfas_nv bfas_nv9 bfas_nw bfas_oi bfas_oo
## alpha 0.8705236 0.9131165 0.9049279 0.8847419 0.8329141 0.8025353
## bfi_a bfi_a6 bfi_c bfi_d_scale bfi_e bfi_hp8
## alpha 0.8117976 0.8028806 0.8218647 0.8056326 0.8749207 0.665913
## bfi_n bfi_o bfi_s_scale hrz_col hrz_ind usi
## alpha 0.8745566 0.8100603 0.7937251 0.7041649 0.5645062 0.6852414
## vrt_col vrt_ind
## alpha 0.7266396 0.6538177
## mvi
## alpha 0.6034461
Note: I use the identification strategy recommended by Widman, Ferrer, and Conger (2010) and set the intercept for the Wave 1 latent variable to 0, and the variance of the Wave 1 latent variable to 1 for each group.
This is an example of the measurement model diagram, using Horizontal Collectivism, for one group demonstrating constraints for the strict measurement invariance model. Paths with the same label are constrained to have the same path weight, and in the strict invariance model, all labeled path weights must be the same for each decade group. The residual covariances are an exception: the constraint imposed is that residual covariance is the same across the same time-lag, for the same indicator (so e.g., cov(aind9, bind9) = cov(bind9, cind9), and cov(aind9, cind9) = cov(bind9, dind9)), but these are not constrained to be the same across group. Since this constraint is imposed in every factorial invariance model tested, it does not affect the fit comparisons.
## hrz_col_W1 ~ 0*1
## hrz_col_W1 ~~ 1*hrz_col_W1
## hrz_col_W1 =~ c(L1, L1, L1, L1)*aind9 + c(L2, L2, L2, L2)*aind10 + c(L3, L3, L3, L3)*aind11 + c(L4, L4, L4, L4)*aind12
## hrz_col_W2 =~ c(L1, L1, L1, L1)*bind9 + c(L2, L2, L2, L2)*bind10 + c(L3, L3, L3, L3)*bind11 + c(L4, L4, L4, L4)*bind12
## hrz_col_W3 =~ c(L1, L1, L1, L1)*cind9 + c(L2, L2, L2, L2)*cind10 + c(L3, L3, L3, L3)*cind11 + c(L4, L4, L4, L4)*cind12
## hrz_col_W4 =~ c(L1, L1, L1, L1)*dind9 + c(L2, L2, L2, L2)*dind10 + c(L3, L3, L3, L3)*dind11 + c(L4, L4, L4, L4)*dind12
##
## #---
##
## aind9 ~ c(int_1, int_1, int_1, int_1)*1
## bind9 ~ c(int_1, int_1, int_1, int_1)*1
## cind9 ~ c(int_1, int_1, int_1, int_1)*1
## dind9 ~ c(int_1, int_1, int_1, int_1)*1
##
## aind10 ~ c(int_2, int_2, int_2, int_2)*1
## bind10 ~ c(int_2, int_2, int_2, int_2)*1
## cind10 ~ c(int_2, int_2, int_2, int_2)*1
## dind10 ~ c(int_2, int_2, int_2, int_2)*1
##
## aind11 ~ c(int_3, int_3, int_3, int_3)*1
## bind11 ~ c(int_3, int_3, int_3, int_3)*1
## cind11 ~ c(int_3, int_3, int_3, int_3)*1
## dind11 ~ c(int_3, int_3, int_3, int_3)*1
##
## aind12 ~ c(int_4, int_4, int_4, int_4)*1
## bind12 ~ c(int_4, int_4, int_4, int_4)*1
## cind12 ~ c(int_4, int_4, int_4, int_4)*1
## dind12 ~ c(int_4, int_4, int_4, int_4)*1
##
## #---
##
## aind9 ~~ c(v_1, v_1, v_1, v_1)*aind9
## bind9 ~~ c(v_1, v_1, v_1, v_1)*bind9
## cind9 ~~ c(v_1, v_1, v_1, v_1)*cind9
## dind9 ~~ c(v_1, v_1, v_1, v_1)*dind9
##
## aind10 ~~ c(v_2, v_2, v_2, v_2)*aind10
## bind10 ~~ c(v_2, v_2, v_2, v_2)*bind10
## cind10 ~~ c(v_2, v_2, v_2, v_2)*cind10
## dind10 ~~ c(v_2, v_2, v_2, v_2)*dind10
##
## aind11 ~~ c(v_3, v_3, v_3, v_3)*aind11
## bind11 ~~ c(v_3, v_3, v_3, v_3)*bind11
## cind11 ~~ c(v_3, v_3, v_3, v_3)*cind11
## dind11 ~~ c(v_3, v_3, v_3, v_3)*dind11
##
## aind12 ~~ c(v_4, v_4, v_4, v_4)*aind12
## bind12 ~~ c(v_4, v_4, v_4, v_4)*bind12
## cind12 ~~ c(v_4, v_4, v_4, v_4)*cind12
## dind12 ~~ c(v_4, v_4, v_4, v_4)*dind12
##
## #---
##
## aind9 ~~ bind9
## aind9 ~~ cind9
## aind9 ~~ dind9
## bind9 ~~ cind9
## bind9 ~~ dind9
## cind9 ~~ dind9
##
## aind10 ~~ bind10
## aind10 ~~ cind10
## aind10 ~~ dind10
## bind10 ~~ cind10
## bind10 ~~ dind10
## cind10 ~~ dind10
##
## aind11 ~~ bind11
## aind11 ~~ cind11
## aind11 ~~ dind11
## bind11 ~~ cind11
## bind11 ~~ dind11
## cind11 ~~ dind11
##
## aind12 ~~ bind12
## aind12 ~~ cind12
## aind12 ~~ dind12
## bind12 ~~ cind12
## bind12 ~~ dind12
## cind12 ~~ dind12
To determine the invariance of measurement over groups, we can examine the \(\chi^2\) test. But this is often an overly strict test with a large sample size. Relative change in AIC and BIC (with lower values, and negative changes, being better) help guide interpretation by incorporating information about the number of parameters (AIC, BIC) and sample size (BIC). Kang, McNeish, & Hancock (2016) recommend using McDonald’s non-centrality parameter (McDonald, 1989) because it is not influenced by complexity, sample size, or measurement quality. Their simulation study indicates that under the null of no difference in model fit, a difference in the MFI, \(\Delta\text{MFI}\), of < -.007 occurs in fewer than 5% of cases, and < -.01 in less that 1% of cases. They also caution against using cutoffs.
Note: The baseline model adds to the strict longitudinal invariance model the additional constraint that covariance among residuals for the same item with the same lag distance must be the same.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 798 | 536 | 0.973 | 0.860 | 0.048 [0.041, 0.054] | |||||
| 2 | long_metric | 864 | 584 | -30.4 | -259.1 | 0.971 | -0.002 | 0.851 | -0.009 | 0.047 [0.040, 0.054] | |
| 3 | long_strong | 930 | 632 | -29.3 | -258.0 | 0.969 | -0.002 | 0.842 | -0.009 | 0.047 [0.040, 0.053] | |
| 4 | long_strict | 1015 | 692 | -35.4 | -321.2 | 0.966 | -0.003 | 0.830 | -0.012 | -0.030 | 0.046 [0.040, 0.052] |
| 5 | metric | 1039 | 707 | -5.8 | -77.3 | 0.965 | -0.001 | 0.825 | -0.004 | -0.025 | 0.047 [0.040, 0.053] |
| 6 | strong | 1079 | 722 | 10.2 | -61.3 | 0.963 | -0.003 | 0.814 | -0.012 | -0.028 | 0.048 [0.042, 0.054] |
| 7 | strict | 1109 | 737 | -0.4 | -71.9 | 0.961 | -0.002 | 0.807 | -0.007 | -0.023 | 0.048 [0.042, 0.054] |
Strong longitudnal invariance. Metric invariance between groups is well supported.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | NA [NA, NA] | |||||||||
| 2 | long_metric | 1456 | 900 | 0.930 | 0.725 | 0.053 [0.048, 0.058] | |||||
| 3 | long_strong | 1542 | 960 | -34.1 | -320.0 | 0.927 | -0.003 | 0.715 | -0.011 | 0.053 [0.048, 0.058] | |
| 4 | long_strict | NA [NA, NA] | |||||||||
| 5 | metric | 1656 | 1050 | 0.924 | 0.705 | -0.020 | 0.052 [0.047, 0.056] | ||||
| 6 | strong | 1711 | 1068 | 18.6 | -67.2 | 0.920 | -0.005 | 0.690 | -0.015 | -0.024 | 0.053 [0.048, 0.057] |
| 7 | strict | 1751 | 1086 | 4.5 | -81.2 | 0.917 | -0.003 | 0.681 | -0.009 | 0.053 [0.049, 0.058] |
Possibly problematic. Unconstrained model does not converge. MFI may be too low for accurate model comparison.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 427 | 296 | 0.973 | 0.927 | 0.045 [0.035, 0.054] | |||||
| 2 | long_metric | 480 | 332 | -18.6 | -190.1 | 0.969 | -0.004 | 0.918 | -0.009 | 0.045 [0.036, 0.054] | |
| 3 | long_strong | 553 | 368 | 0.4 | -171.1 | 0.962 | -0.008 | 0.899 | -0.019 | 0.048 [0.040, 0.056] | |
| 4 | long_strict | 609 | 416 | -40.1 | -268.8 | 0.960 | -0.002 | 0.895 | -0.004 | -0.032 | 0.046 [0.038, 0.054] |
| 5 | metric | 641 | 428 | 8.0 | -49.1 | 0.956 | -0.004 | 0.884 | -0.010 | -0.033 | 0.048 [0.040, 0.055] |
| 6 | strong | 712 | 440 | 47.0 | -10.2 | 0.944 | -0.012 | 0.855 | -0.030 | -0.044 | 0.053 [0.046, 0.061] |
| 7 | strict | 755 | 452 | 19.5 | -37.7 | 0.937 | -0.007 | 0.839 | -0.015 | -0.055 | 0.056 [0.049, 0.063] |
Longitudinal metric invariance is supported. Group metric invariance is on the recommended cutoff.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 474 | 296 | 0.942 | 0.902 | 0.053 [0.044, 0.061] | |||||
| 2 | long_metric | 507 | 332 | -39.5 | -211.0 | 0.944 | 0.001 | 0.904 | 0.002 | 0.049 [0.041, 0.058] | |
| 3 | long_strong | 551 | 368 | -27.3 | -198.8 | 0.941 | -0.003 | 0.900 | -0.005 | 0.048 [0.039, 0.056] | |
| 4 | long_strict | 616 | 416 | -31.0 | -259.7 | 0.935 | -0.005 | 0.891 | -0.009 | -0.011 | 0.047 [0.039, 0.055] |
| 5 | metric | 634 | 428 | -6.2 | -63.4 | 0.933 | -0.002 | 0.888 | -0.003 | -0.016 | 0.047 [0.039, 0.055] |
| 6 | strong | 661 | 440 | 3.1 | -54.1 | 0.928 | -0.005 | 0.880 | -0.008 | -0.019 | 0.048 [0.040, 0.056] |
| 7 | strict | 676 | 452 | -9.6 | -66.7 | 0.928 | -0.001 | 0.879 | -0.001 | -0.012 | 0.048 [0.040, 0.055] |
Invariant.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 22996 | 8408 | 0.599 | 0.000 | 0.090 [0.088, 0.091] | |||||
| 2 | long_metric | 23260 | 8600 | -119.9 | -1034.6 | 0.597 | -0.002 | 0.000 | -0.000 | 0.089 [0.087, 0.090] | |
| 3 | long_strong | 23513 | 8792 | -131.4 | -1046.1 | 0.596 | -0.002 | 0.000 | -0.000 | 0.088 [0.087, 0.089] | |
| 4 | long_strict | 23793 | 8996 | -128.2 | -1100.0 | 0.594 | -0.002 | 0.000 | -0.000 | -0.000 | 0.087 [0.086, 0.089] |
| 5 | metric | 23861 | 9047 | -33.8 | -276.7 | 0.593 | -0.000 | 0.000 | -0.000 | -0.000 | 0.087 [0.086, 0.088] |
| 6 | strong | 24081 | 9098 | 117.9 | -125.1 | 0.588 | -0.005 | 0.000 | -0.000 | -0.000 | 0.087 [0.086, 0.089] |
| 7 | strict | 24249 | 9149 | 66.0 | -176.9 | 0.585 | -0.003 | 0.000 | -0.000 | -0.000 | 0.087 [0.086, 0.089] |
Possibly problematic.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | NA [NA, NA] | |||||||||
| 2 | long_metric | 1731 | 900 | 0.876 | 0.619 | 0.065 [0.061, 0.070] | |||||
| 3 | long_strong | 1814 | 960 | -36.3 | -322.1 | 0.872 | -0.004 | 0.611 | -0.008 | 0.064 [0.060, 0.069] | |
| 4 | long_strict | 1914 | 1032 | -44.1 | -387.1 | 0.868 | -0.004 | 0.601 | -0.010 | 0.063 [0.058, 0.067] | |
| 5 | metric | 1947 | 1050 | -3.7 | -89.5 | 0.866 | -0.002 | 0.596 | -0.005 | -0.023 | 0.063 [0.058, 0.067] |
| 6 | strong | 2015 | 1068 | 32.8 | -52.9 | 0.858 | -0.008 | 0.579 | -0.017 | -0.032 | 0.064 [0.060, 0.068] |
| 7 | strict | 2083 | 1086 | 31.0 | -54.7 | 0.851 | -0.007 | 0.563 | -0.016 | -0.038 | 0.065 [0.061, 0.069] |
The unconstrained model did not converge. Strict longitudinal invariance may be supported. Group metric invariance is supported, but not strong group invariance.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 352 | 296 | 0.988 | 0.968 | 0.029 [0.014, 0.041] | |||||
| 2 | long_metric | 376 | 332 | -47.4 | -218.9 | 0.991 | 0.002 | 0.975 | 0.006 | 0.025 [0.003, 0.037] | |
| 3 | long_strong | 413 | 368 | -35.0 | -206.5 | 0.990 | -0.000 | 0.974 | -0.001 | 0.024 [0.000, 0.035] | |
| 4 | long_strict | 473 | 416 | -35.7 | -264.3 | 0.988 | -0.003 | 0.967 | -0.007 | -0.001 | 0.025 [0.009, 0.036] |
| 5 | metric | 506 | 428 | 8.9 | -48.3 | 0.983 | -0.004 | 0.956 | -0.012 | -0.019 | 0.029 [0.017, 0.039] |
| 6 | strong | 565 | 440 | 35.1 | -22.1 | 0.973 | -0.010 | 0.930 | -0.026 | -0.044 | 0.036 [0.027, 0.045] |
| 7 | strict | 589 | 452 | -0.8 | -57.9 | 0.971 | -0.002 | 0.924 | -0.006 | -0.043 | 0.037 [0.028, 0.046] |
Longitudinal strict invariance is well supported. Group metric invariance is not supported.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 343 | 296 | 0.989 | 0.973 | 0.027 [0.009, 0.039] | |||||
| 2 | long_metric | 380 | 332 | -35.2 | -206.7 | 0.989 | -0.000 | 0.973 | -0.000 | 0.026 [0.007, 0.037] | |
| 3 | long_strong | 413 | 368 | -38.9 | -210.4 | 0.990 | 0.001 | 0.974 | 0.002 | 0.024 [0.000, 0.035] | |
| 4 | long_strict | 468 | 416 | -40.8 | -269.5 | 0.988 | -0.002 | 0.970 | -0.004 | -0.003 | 0.024 [0.006, 0.035] |
| 5 | metric | 489 | 428 | -3.6 | -60.7 | 0.986 | -0.002 | 0.966 | -0.005 | -0.007 | 0.026 [0.011, 0.036] |
| 6 | strong | 550 | 440 | 37.2 | -20.0 | 0.975 | -0.011 | 0.938 | -0.027 | -0.036 | 0.034 [0.024, 0.043] |
| 7 | strict | 563 | 452 | -10.9 | -68.1 | 0.975 | -0.000 | 0.938 | -0.001 | -0.032 | 0.034 [0.024, 0.042] |
Longitudinal strict invaraince is well supported. Group metric invariance is well supported.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 3379 | 2136 | 0.904 | 0.488 | 0.052 [0.048, 0.055] | |||||
| 2 | long_metric | 3481 | 2232 | -89.9 | -547.4 | 0.904 | -0.000 | 0.487 | -0.002 | 0.051 [0.048, 0.054] | |
| 3 | long_strong | 3576 | 2328 | -96.9 | -554.4 | 0.904 | 0.000 | 0.487 | 0.000 | 0.050 [0.046, 0.053] | |
| 4 | long_strict | 3733 | 2436 | -58.6 | -573.2 | 0.900 | -0.004 | 0.473 | -0.014 | -0.015 | 0.050 [0.046, 0.053] |
| 5 | metric | 3763 | 2463 | -25.0 | -153.6 | 0.900 | -0.000 | 0.473 | -0.001 | -0.014 | 0.049 [0.046, 0.052] |
| 6 | strong | 3845 | 2490 | 28.6 | -100.0 | 0.895 | -0.004 | 0.458 | -0.015 | -0.029 | 0.050 [0.047, 0.053] |
| 7 | strict | 3938 | 2517 | 39.0 | -89.6 | 0.890 | -0.005 | 0.441 | -0.017 | -0.033 | 0.051 [0.048, 0.054] |
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 3054 | 2136 | 0.925 | 0.589 | 0.045 [0.041, 0.048] | |||||
| 2 | long_metric | 3169 | 2232 | -77.7 | -535.2 | 0.924 | -0.001 | 0.583 | -0.006 | 0.044 [0.040, 0.047] | |
| 3 | long_strong | 3313 | 2328 | -47.3 | -504.7 | 0.920 | -0.004 | 0.567 | -0.016 | 0.044 [0.041, 0.048] | |
| 4 | long_strict | 3425 | 2436 | -104.8 | -619.4 | 0.919 | -0.000 | 0.565 | -0.001 | -0.023 | 0.043 [0.040, 0.047] |
| 5 | metric | 3459 | 2463 | -19.7 | -148.3 | 0.919 | -0.001 | 0.563 | -0.002 | -0.020 | 0.043 [0.040, 0.047] |
| 6 | strong | 3514 | 2490 | 0.8 | -127.9 | 0.916 | -0.002 | 0.554 | -0.009 | -0.012 | 0.044 [0.040, 0.047] |
| 7 | strict | 3564 | 2517 | -3.9 | -132.6 | 0.915 | -0.002 | 0.547 | -0.007 | -0.019 | 0.044 [0.040, 0.047] |
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 2504 | 1640 | 0.937 | 0.608 | 0.049 [0.045, 0.053] | |||||
| 2 | long_metric | 2592 | 1724 | -79.6 | -479.8 | 0.937 | -0.000 | 0.606 | -0.002 | 0.048 [0.044, 0.052] | |
| 3 | long_strong | 2703 | 1808 | -57.2 | -457.5 | 0.935 | -0.002 | 0.597 | -0.009 | 0.048 [0.044, 0.051] | |
| 4 | long_strict | 2799 | 1904 | -96.5 | -553.9 | 0.935 | 0.000 | 0.597 | 0.000 | -0.011 | 0.047 [0.043, 0.050] |
| 5 | metric | 2820 | 1928 | -27.1 | -141.5 | 0.935 | 0.000 | 0.598 | 0.001 | -0.008 | 0.046 [0.042, 0.050] |
| 6 | strong | 2880 | 1952 | 12.1 | -102.2 | 0.933 | -0.003 | 0.586 | -0.012 | -0.011 | 0.047 [0.043, 0.050] |
| 7 | strict | 2918 | 1976 | -9.7 | -124.1 | 0.932 | -0.001 | 0.581 | -0.005 | -0.016 | 0.047 [0.043, 0.050] |
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 2977 | 1640 | 0.921 | 0.463 | 0.061 [0.058, 0.065] | |||||
| 2 | long_metric | 3044 | 1724 | -100.9 | -501.2 | 0.922 | 0.001 | 0.467 | 0.005 | 0.059 [0.056, 0.063] | |
| 3 | long_strong | 3140 | 1808 | -72.0 | -472.2 | 0.921 | -0.001 | 0.464 | -0.003 | 0.058 [0.055, 0.062] | |
| 4 | long_strict | 3243 | 1904 | -89.1 | -546.5 | 0.920 | -0.000 | 0.462 | -0.002 | -0.001 | 0.057 [0.054, 0.060] |
| 5 | metric | 3276 | 1928 | -14.6 | -129.0 | 0.920 | -0.001 | 0.460 | -0.002 | -0.008 | 0.057 [0.053, 0.060] |
| 6 | strong | 3322 | 1952 | -1.8 | -116.1 | 0.919 | -0.001 | 0.454 | -0.006 | -0.010 | 0.057 [0.054, 0.060] |
| 7 | strict | 3360 | 1976 | -10.4 | -124.7 | 0.918 | -0.001 | 0.450 | -0.004 | -0.012 | 0.057 [0.054, 0.060] |
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 4783 | 2696 | 0.869 | 0.300 | 0.060 [0.057, 0.063] | |||||
| 2 | long_metric | 4888 | 2804 | -110.7 | -625.4 | 0.869 | 0.000 | 0.301 | 0.000 | 0.059 [0.056, 0.061] | |
| 3 | long_strong | 5002 | 2912 | -102.7 | -617.4 | 0.868 | -0.000 | 0.300 | -0.001 | 0.058 [0.055, 0.060] | |
| 4 | long_strict | 5229 | 3032 | -12.4 | -584.2 | 0.862 | -0.007 | 0.282 | -0.018 | -0.018 | 0.058 [0.055, 0.060] |
| 5 | metric | 5274 | 3062 | -15.0 | -158.0 | 0.861 | -0.001 | 0.279 | -0.002 | -0.021 | 0.058 [0.055, 0.060] |
| 6 | strong | 5348 | 3092 | 14.2 | -128.8 | 0.858 | -0.003 | 0.272 | -0.007 | -0.027 | 0.058 [0.055, 0.061] |
| 7 | strict | 5395 | 3122 | -13.2 | -156.2 | 0.857 | -0.001 | 0.270 | -0.003 | -0.012 | 0.058 [0.055, 0.061] |
For some reason lavaan orders the groups like this:
Looking at issues with strict longitudinal invariance.
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| aspfin_W2 | =~ | basp14 | 3 | 3 | 5.40 | 0.14 | 0.11 | 0.1 | 2.80 | 0.39 | (m) |
| aspfin_W3 | =~ | casp12 | 3 | 3 | 5.30 | 0.14 | 0.12 | 0.1 | 2.84 | 0.39 | (m) |
| aspfin_W1 | =~ | aasp14 | 2 | 2 | 5.25 | -0.20 | -0.15 | 0.1 | 1.29 | 0.21 | (m) |
| aspfin_W3 | =~ | casp14 | 4 | 4 | 5.02 | 0.18 | 0.12 | 0.1 | 1.60 | 0.24 | (m) |
| aspfin_W1 | =~ | aasp12 | 4 | 4 | 3.65 | -0.11 | -0.09 | 0.1 | 3.30 | 0.44 | (i) |
| aspfin_W1 | =~ | aasp16 | 3 | 3 | 3.51 | 0.09 | 0.08 | 0.1 | 4.34 | 0.55 | (i) |
| aspfin_W4 | =~ | dasp14 | 1 | 1 | 3.41 | 0.10 | 0.08 | 0.1 | 3.38 | 0.45 | (i) |
| aspfin_W4 | =~ | dasp12 | 1 | 1 | 3.24 | 0.08 | 0.07 | 0.1 | 4.79 | 0.59 | (i) |
| aspfin_W1 | =~ | aasp13 | 4 | 4 | 2.86 | 0.08 | 0.07 | 0.1 | 4.67 | 0.58 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| dasp14 | ~1 | 1 | 1 | 19.28 | -0.25 | -0.18 | 0.1 | 3.10 | 0.42 | (m) | |
| dasp14 | ~1 | 3 | 3 | 8.27 | -0.19 | -0.14 | 0.1 | 2.26 | 0.32 | (m) | |
| aasp14 | ~1 | 4 | 4 | 7.42 | 0.17 | 0.13 | 0.1 | 2.61 | 0.37 | (m) | |
| aasp14 | ~1 | 3 | 3 | 6.42 | 0.15 | 0.11 | 0.1 | 2.91 | 0.40 | (m) | |
| aasp13 | ~1 | 2 | 2 | 6.21 | -0.14 | -0.13 | 0.1 | 3.05 | 0.42 | (m) | |
| aspfin_W1 | ~1 | 1 | 1 | 4.72 | 0.17 | 0.17 | 0.1 | 1.73 | 0.26 | (m) | |
| basp16 | ~1 | 1 | 1 | 4.09 | -0.10 | -0.09 | 0.1 | 4.50 | 0.56 | (m) | |
| dasp16 | ~1 | 3 | 3 | 3.29 | 0.10 | 0.09 | 0.1 | 3.22 | 0.43 | (i) | |
| casp15 | ~1 | 4 | 4 | 3.14 | -0.12 | -0.10 | 0.1 | 2.26 | 0.32 | (i) | |
| dasp15 | ~1 | 1 | 1 | 3.00 | 0.08 | 0.07 | 0.1 | 4.44 | 0.56 | (i) | |
| aasp12 | ~1 | 4 | 4 | 2.86 | -0.09 | -0.07 | 0.1 | 3.68 | 0.48 | (i) | |
| aasp16 | ~1 | 2 | 2 | 2.83 | 0.10 | 0.09 | 0.1 | 2.62 | 0.37 | (i) | |
| aasp14 | ~1 | 1 | 1 | 2.54 | 0.08 | 0.06 | 0.1 | 3.73 | 0.49 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| aasp16 | ~~ | aasp16 | 4 | 4 | 13.40 | 0.18 | 0.36 | 0.1 | 4.37 | 0.55 | (m) |
| casp12 | ~~ | casp12 | 2 | 2 | 3.72 | 0.15 | 0.58 | 0.1 | 1.71 | 0.26 | (i) |
| casp16 | ~~ | casp16 | 4 | 4 | 3.48 | -0.09 | -0.41 | 0.1 | 4.30 | 0.55 | (i) |
| dasp16 | ~~ | dasp16 | 3 | 3 | 3.13 | 0.10 | 0.35 | 0.1 | 3.25 | 0.44 | (i) |
| aspfin_W1 | ~~ | aspfin_W1 | 1 | 1 | 2.78 | 0.19 | 1.00 | 0.1 | 0.76 | 0.14 | (i) |
| basp13 | ~~ | basp13 | 4 | 4 | 2.59 | 0.06 | 0.24 | 0.1 | 6.64 | 0.73 | (i) |
| casp13 | ~~ | casp13 | 3 | 3 | 2.56 | -0.05 | -0.21 | 0.1 | 9.38 | 0.86 | (nm) |
| basp13 | ~~ | basp13 | 1 | 1 | 2.51 | -0.05 | -0.23 | 0.1 | 10.01 | 0.89 | (nm) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| bfa_mt_W1 | =~ | abfas117 | 2 | 2 | 5.77 | -0.20 | -0.18 | 0.1 | 1.49 | 0.23 | (m) |
| bfa_mt_W2 | =~ | bbfas113 | 3 | 3 | 4.87 | 0.14 | 0.11 | 0.1 | 2.39 | 0.34 | (m) |
| bfa_mt_W4 | =~ | dbfas113 | 4 | 4 | 4.16 | -0.20 | -0.15 | 0.1 | 1.02 | 0.17 | (m) |
| bfa_mt_W1 | =~ | abfas116 | 2 | 2 | 4.10 | 0.17 | 0.15 | 0.1 | 1.39 | 0.22 | (m) |
| bfa_mt_W1 | =~ | abfas115 | 2 | 2 | 2.95 | 0.14 | 0.12 | 0.1 | 1.45 | 0.23 | (i) |
| bfa_mt_W4 | =~ | dbfas118 | 3 | 3 | 2.56 | -0.12 | -0.10 | 0.1 | 1.85 | 0.27 | (i) |
| bfa_mt_W3 | =~ | cbfas117 | 1 | 1 | 2.53 | 0.09 | 0.09 | 0.1 | 2.86 | 0.39 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| bfa_mt_W1 | ~1 | 1 | 1 | 12.43 | -0.28 | -0.28 | 0.1 | 1.59 | 0.24 | (m) | |
| bfa_mt_W1 | ~1 | 2 | 2 | 10.52 | 0.34 | 0.34 | 0.1 | 0.90 | 0.16 | (m) | |
| abfas118 | ~1 | 2 | 2 | 7.81 | 0.21 | 0.18 | 0.1 | 1.78 | 0.27 | (m) | |
| bbfas113 | ~1 | 1 | 1 | 7.06 | 0.14 | 0.11 | 0.1 | 3.50 | 0.46 | (m) | |
| abfas113 | ~1 | 1 | 1 | 6.71 | 0.14 | 0.11 | 0.1 | 3.27 | 0.44 | (m) | |
| dbfas113 | ~1 | 4 | 4 | 6.41 | -0.20 | -0.17 | 0.1 | 1.54 | 0.24 | (m) | |
| dbfas114 | ~1 | 1 | 1 | 6.38 | 0.12 | 0.11 | 0.1 | 4.34 | 0.55 | (m) | |
| dbfas118 | ~1 | 4 | 4 | 6.20 | -0.19 | -0.18 | 0.1 | 1.74 | 0.26 | (m) | |
| bfa_mt_W1 | ~1 | 4 | 4 | 6.05 | 0.22 | 0.22 | 0.1 | 1.24 | 0.20 | (m) | |
| cbfas113 | ~1 | 1 | 1 | 5.19 | -0.13 | -0.10 | 0.1 | 3.05 | 0.42 | (m) | |
| cbfas113 | ~1 | 2 | 2 | 4.66 | -0.23 | -0.18 | 0.1 | 0.88 | 0.16 | (m) | |
| bbfas114 | ~1 | 3 | 3 | 4.48 | 0.11 | 0.10 | 0.1 | 3.92 | 0.51 | (m) | |
| dbfas116 | ~1 | 1 | 1 | 4.34 | 0.12 | 0.10 | 0.1 | 2.91 | 0.40 | (m) | |
| cbfas114 | ~1 | 1 | 1 | 4.12 | -0.10 | -0.09 | 0.1 | 4.52 | 0.57 | (m) | |
| bbfas113 | ~1 | 3 | 3 | 3.78 | -0.11 | -0.09 | 0.1 | 2.93 | 0.40 | (i) | |
| abfas115 | ~1 | 3 | 3 | 3.53 | 0.11 | 0.09 | 0.1 | 2.92 | 0.40 | (i) | |
| cbfas116 | ~1 | 1 | 1 | 3.47 | -0.11 | -0.09 | 0.1 | 3.00 | 0.41 | (i) | |
| abfas118 | ~1 | 4 | 4 | 2.53 | 0.10 | 0.08 | 0.1 | 2.75 | 0.38 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| cbfas118 | ~~ | cbfas118 | 2 | 2 | 6.19 | 0.26 | 0.42 | 0.1 | 0.92 | 0.16 | (m) |
| dbfas118 | ~~ | dbfas118 | 3 | 3 | 6.10 | 0.19 | 0.49 | 0.1 | 1.65 | 0.25 | (m) |
| bbfas116 | ~~ | bbfas116 | 2 | 2 | 3.31 | 0.20 | 0.59 | 0.1 | 0.81 | 0.15 | (i) |
| cbfas117 | ~~ | cbfas117 | 4 | 4 | 3.06 | 0.14 | 0.68 | 0.1 | 1.56 | 0.24 | (i) |
| cbfas118 | ~~ | cbfas118 | 3 | 3 | 3.02 | -0.13 | -0.47 | 0.1 | 1.79 | 0.27 | (i) |
| dbfas115 | ~~ | dbfas115 | 1 | 1 | 2.99 | -0.13 | -0.53 | 0.1 | 1.82 | 0.27 | (i) |
| dbfas114 | ~~ | dbfas114 | 3 | 3 | 2.50 | 0.08 | 0.63 | 0.1 | 3.83 | 0.50 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| hrz_col_W1 | =~ | aind9 | 1 | 1 | 7.32 | 0.13 | 0.13 | 0.1 | 4.50 | 0.56 | (m) |
| hrz_col_W2 | =~ | bind11 | 2 | 2 | 4.93 | 0.25 | 0.21 | 0.1 | 0.78 | 0.14 | (m) |
| hrz_col_W2 | =~ | bind10 | 1 | 1 | 4.71 | -0.10 | -0.11 | 0.1 | 4.86 | 0.60 | (m) |
| hrz_col_W1 | =~ | aind12 | 3 | 3 | 4.42 | -0.09 | -0.11 | 0.1 | 5.42 | 0.64 | (m) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| hrz_col_W1 | ~1 | 1 | 1 | 25.80 | -0.42 | -0.42 | 0.1 | 1.48 | 0.23 | (m) | |
| hrz_col_W1 | ~1 | 2 | 2 | 21.08 | 0.50 | 0.50 | 0.1 | 0.83 | 0.15 | (m) | |
| aind9 | ~1 | 1 | 1 | 21.06 | -0.20 | -0.20 | 0.1 | 5.51 | 0.65 | (m) | |
| aind11 | ~1 | 1 | 1 | 7.87 | 0.14 | 0.13 | 0.1 | 4.03 | 0.52 | (m) | |
| cind9 | ~1 | 2 | 2 | 7.81 | 0.15 | 0.17 | 0.1 | 3.30 | 0.44 | (m) | |
| dind11 | ~1 | 1 | 1 | 7.23 | -0.15 | -0.14 | 0.1 | 3.02 | 0.41 | (m) | |
| bind9 | ~1 | 1 | 1 | 6.79 | -0.11 | -0.12 | 0.1 | 5.19 | 0.62 | (m) | |
| bind12 | ~1 | 3 | 3 | 5.07 | -0.10 | -0.13 | 0.1 | 4.77 | 0.59 | (m) | |
| aind12 | ~1 | 2 | 2 | 4.78 | 0.11 | 0.14 | 0.1 | 3.63 | 0.48 | (m) | |
| aind12 | ~1 | 4 | 4 | 4.66 | 0.09 | 0.11 | 0.1 | 5.63 | 0.66 | (m) | |
| aind10 | ~1 | 2 | 2 | 4.24 | 0.11 | 0.13 | 0.1 | 3.39 | 0.45 | (m) | |
| dind12 | ~1 | 4 | 4 | 3.41 | -0.10 | -0.13 | 0.1 | 3.44 | 0.46 | (i) | |
| aind12 | ~1 | 3 | 3 | 3.03 | 0.07 | 0.08 | 0.1 | 6.64 | 0.73 | (i) | |
| bind10 | ~1 | 1 | 1 | 2.83 | 0.07 | 0.08 | 0.1 | 5.78 | 0.67 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| aind9 | ~~ | aind9 | 1 | 1 | 10.03 | 0.14 | 0.55 | 0.1 | 5.13 | 0.62 | (m) |
| hrz_col_W1 | ~~ | hrz_col_W1 | 4 | 4 | 7.75 | -0.42 | -1.00 | 0.1 | 0.44 | 0.10 | (m) |
| hrz_col_W1 | ~~ | hrz_col_W1 | 1 | 1 | 6.68 | 0.35 | 1.00 | 0.1 | 0.56 | 0.12 | (m) |
| dind11 | ~~ | dind11 | 1 | 1 | 3.28 | 0.12 | 0.78 | 0.1 | 2.12 | 0.31 | (i) |
| aind12 | ~~ | aind12 | 4 | 4 | 2.81 | -0.06 | -0.60 | 0.1 | 8.24 | 0.82 | (nm) |
| aind10 | ~~ | aind10 | 2 | 2 | 2.77 | -0.08 | -0.43 | 0.1 | 4.61 | 0.57 | (i) |
| aind10 | ~~ | aind10 | 3 | 3 | 2.67 | 0.06 | 0.43 | 0.1 | 6.51 | 0.72 | (i) |
| bind12 | ~~ | bind12 | 1 | 1 | 2.61 | 0.06 | 0.61 | 0.1 | 6.93 | 0.75 | (i) |
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| hrz_ind_W2 | =~ | bind3 | 3 | 3 | 5.81 | 0.19 | 0.17 | 0.1 | 1.68 | 0.25 | (m) |
| hrz_ind_W2 | =~ | bind1 | 3 | 3 | 3.16 | -0.10 | -0.12 | 0.1 | 3.21 | 0.43 | (i) |
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| aind4 | ~1 | 1 | 1 | 5.94 | 0.10 | 0.12 | 0.1 | 5.51 | 0.65 | (m) | |
| bind1 | ~1 | 1 | 1 | 4.46 | -0.09 | -0.10 | 0.1 | 6.05 | 0.69 | (m) | |
| dind4 | ~1 | 1 | 1 | 4.40 | -0.10 | -0.12 | 0.1 | 4.52 | 0.57 | (m) | |
| cind1 | ~1 | 2 | 2 | 3.77 | -0.15 | -0.19 | 0.1 | 1.79 | 0.27 | (i) | |
| dind1 | ~1 | 2 | 2 | 3.26 | 0.13 | 0.16 | 0.1 | 1.95 | 0.29 | (i) | |
| dind3 | ~1 | 4 | 4 | 3.08 | -0.12 | -0.11 | 0.1 | 2.15 | 0.31 | (i) | |
| aind2 | ~1 | 1 | 1 | 3.08 | -0.08 | -0.08 | 0.1 | 4.51 | 0.57 | (i) | |
| aind3 | ~1 | 1 | 1 | 2.82 | 0.09 | 0.08 | 0.1 | 3.77 | 0.49 | (i) | |
| dind3 | ~1 | 3 | 3 | 2.81 | -0.11 | -0.10 | 0.1 | 2.18 | 0.32 | (i) | |
| cind4 | ~1 | 4 | 4 | 2.78 | -0.11 | -0.13 | 0.1 | 2.28 | 0.33 | (i) | |
| cind2 | ~1 | 2 | 2 | 2.68 | 0.14 | 0.14 | 0.1 | 1.43 | 0.22 | (i) |
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| cind1 | ~~ | cind1 | 2 | 2 | 6.52 | 0.18 | 0.69 | 0.1 | 1.97 | 0.29 | (m) |
| cind1 | ~~ | cind1 | 3 | 3 | 3.81 | 0.10 | 0.63 | 0.1 | 4.00 | 0.52 | (i) |
| dind4 | ~~ | dind4 | 2 | 2 | 2.88 | 0.13 | 0.91 | 0.1 | 1.62 | 0.25 | (i) |
It’s not clear that we can trust the invariance tests for this scale.
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W2 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W3 [in block 4]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| usi_W3 | =~ | cusi7 | 1 | 1 | 4.21 | -0.14 | -0.11 | 0.1 | 2.30 | 0.33 | (m) |
| usi_W2 | =~ | busi1 | 4 | 4 | 3.83 | 0.14 | 0.13 | 0.1 | 1.93 | 0.28 | (i) |
| usi_W4 | =~ | dusi6 | 3 | 3 | 3.41 | 0.15 | 0.14 | 0.1 | 1.55 | 0.24 | (i) |
| usi_W2 | =~ | busi5 | 4 | 4 | 3.13 | -0.10 | -0.10 | 0.1 | 3.37 | 0.45 | (i) |
| usi_W2 | =~ | busi3 | 3 | 3 | 2.90 | 0.12 | 0.13 | 0.1 | 1.96 | 0.29 | (i) |
| usi_W2 | =~ | busi2 | 1 | 1 | 2.87 | -0.08 | -0.10 | 0.1 | 4.30 | 0.55 | (i) |
| usi_W1 | =~ | ausi2 | 3 | 3 | 2.54 | -0.09 | -0.10 | 0.1 | 3.51 | 0.47 | (i) |
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W2 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W3 [in block 4]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| usi_W1 | ~1 | 1 | 1 | 21.17 | 0.39 | 0.39 | 0.1 | 1.36 | 0.21 | (m) | |
| ausi1 | ~1 | 1 | 1 | 11.59 | 0.17 | 0.14 | 0.1 | 4.20 | 0.54 | (m) | |
| ausi2 | ~1 | 2 | 2 | 8.96 | 0.18 | 0.21 | 0.1 | 2.82 | 0.39 | (m) | |
| dusi1 | ~1 | 1 | 1 | 8.55 | -0.17 | -0.14 | 0.1 | 3.14 | 0.43 | (m) | |
| usi_W1 | ~1 | 2 | 2 | 7.31 | -0.26 | -0.26 | 0.1 | 1.06 | 0.18 | (m) | |
| ausi1 | ~1 | 3 | 3 | 6.55 | 0.15 | 0.13 | 0.1 | 3.02 | 0.41 | (m) | |
| usi_W1 | ~1 | 4 | 4 | 6.00 | -0.22 | -0.22 | 0.1 | 1.21 | 0.20 | (m) | |
| ausi7 | ~1 | 4 | 4 | 3.84 | -0.14 | -0.11 | 0.1 | 2.07 | 0.30 | (m) | |
| ausi3 | ~1 | 4 | 4 | 3.64 | -0.11 | -0.12 | 0.1 | 2.90 | 0.40 | (i) | |
| dusi1 | ~1 | 2 | 2 | 3.45 | -0.17 | -0.14 | 0.1 | 1.14 | 0.19 | (i) | |
| dusi6 | ~1 | 2 | 2 | 2.88 | -0.17 | -0.16 | 0.1 | 0.94 | 0.16 | (i) | |
| ausi1 | ~1 | 2 | 2 | 2.66 | 0.12 | 0.11 | 0.1 | 1.78 | 0.27 | (i) | |
| cusi1 | ~1 | 3 | 3 | 2.61 | -0.11 | -0.10 | 0.1 | 2.16 | 0.31 | (i) |
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W2 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W3 [in block 4]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| usi_W1 | ~~ | usi_W1 | 2 | 2 | 6.02 | -0.25 | -1.00 | 0.1 | 0.97 | 0.17 | (m) |
| usi_W3 | ~~ | usi_W3 | 2 | 2 | 4.34 | 0.11 | 1.00 | 0.1 | 3.59 | 0.47 | (m) |
| ausi7 | ~~ | ausi7 | 2 | 2 | 3.72 | 0.25 | 0.70 | 0.1 | 0.57 | 0.12 | (i) |
| ausi5 | ~~ | ausi5 | 2 | 2 | 3.72 | -0.11 | -0.70 | 0.1 | 3.05 | 0.42 | (i) |
| ausi1 | ~~ | ausi1 | 3 | 3 | 3.49 | 0.13 | 0.67 | 0.1 | 1.98 | 0.29 | (i) |
| busi6 | ~~ | busi6 | 2 | 2 | 3.36 | -0.20 | -0.71 | 0.1 | 0.83 | 0.15 | (i) |
| busi6 | ~~ | busi6 | 3 | 3 | 3.18 | 0.14 | 0.71 | 0.1 | 1.63 | 0.25 | (i) |
| busi2 | ~~ | busi2 | 1 | 1 | 3.16 | 0.08 | 0.80 | 0.1 | 5.38 | 0.64 | (i) |
| cusi5 | ~~ | cusi5 | 1 | 1 | 3.09 | 0.09 | 0.68 | 0.1 | 4.07 | 0.52 | (i) |
| busi6 | ~~ | busi6 | 4 | 4 | 2.53 | -0.14 | -0.66 | 0.1 | 1.22 | 0.20 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| vrt_col_W3 | =~ | cind14 | 1 | 1 | 6.67 | 0.11 | 0.14 | 0.1 | 5.30 | 0.63 | (m) |
| vrt_col_W3 | =~ | cind14 | 4 | 4 | 5.34 | -0.14 | -0.16 | 0.1 | 2.87 | 0.39 | (m) |
| vrt_col_W1 | =~ | aind14 | 4 | 4 | 5.16 | -0.10 | -0.12 | 0.1 | 5.10 | 0.62 | (m) |
| vrt_col_W1 | =~ | aind15 | 2 | 2 | 2.66 | 0.12 | 0.11 | 0.1 | 1.75 | 0.26 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| cind14 | ~1 | 1 | 1 | 8.53 | -0.14 | -0.15 | 0.1 | 4.26 | 0.54 | (m) | |
| aind13 | ~1 | 1 | 1 | 6.90 | -0.12 | -0.11 | 0.1 | 4.65 | 0.58 | (m) | |
| aind15 | ~1 | 1 | 1 | 5.04 | 0.11 | 0.10 | 0.1 | 4.47 | 0.56 | (m) | |
| aind16 | ~1 | 2 | 2 | 4.66 | 0.15 | 0.16 | 0.1 | 2.00 | 0.29 | (m) | |
| cind13 | ~1 | 1 | 1 | 4.33 | 0.11 | 0.09 | 0.1 | 3.68 | 0.48 | (m) | |
| vrt_col_W1 | ~1 | 1 | 1 | 4.27 | -0.17 | -0.17 | 0.1 | 1.46 | 0.23 | (m) | |
| cind15 | ~1 | 4 | 4 | 4.00 | -0.12 | -0.11 | 0.1 | 2.70 | 0.38 | (m) | |
| cind13 | ~1 | 2 | 2 | 3.84 | -0.16 | -0.14 | 0.1 | 1.56 | 0.24 | (i) | |
| cind16 | ~1 | 2 | 2 | 3.59 | 0.15 | 0.15 | 0.1 | 1.64 | 0.25 | (i) | |
| bind16 | ~1 | 1 | 1 | 3.45 | -0.10 | -0.10 | 0.1 | 3.78 | 0.49 | (i) | |
| bind13 | ~1 | 1 | 1 | 3.23 | 0.09 | 0.08 | 0.1 | 3.94 | 0.51 | (i) | |
| aind16 | ~1 | 1 | 1 | 2.68 | -0.08 | -0.08 | 0.1 | 4.58 | 0.57 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| cind14 | ~~ | cind14 | 1 | 1 | 14.63 | 0.19 | 0.58 | 0.1 | 4.25 | 0.54 | (m) |
| aind13 | ~~ | aind13 | 1 | 1 | 2.79 | 0.09 | 0.54 | 0.1 | 3.62 | 0.48 | (i) |
| aind15 | ~~ | aind15 | 3 | 3 | 2.70 | 0.10 | 0.43 | 0.1 | 2.97 | 0.41 | (i) |
| dind15 | ~~ | dind15 | 1 | 1 | 2.64 | -0.09 | -0.36 | 0.1 | 3.09 | 0.42 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| vrt_ind_W1 | =~ | aind8 | 1 | 1 | 3.29 | 0.11 | 0.09 | 0.1 | 2.94 | 0.40 | (i) |
| vrt_ind_W4 | =~ | dind7 | 4 | 4 | 2.96 | 0.17 | 0.12 | 0.1 | 1.01 | 0.17 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| vrt_ind_W1 | ~1 | 1 | 1 | 9.83 | 0.27 | 0.27 | 0.1 | 1.39 | 0.22 | (m) | |
| vrt_ind_W1 | ~1 | 2 | 2 | 9.27 | -0.34 | -0.34 | 0.1 | 0.78 | 0.14 | (m) | |
| aind8 | ~1 | 1 | 1 | 8.56 | 0.15 | 0.13 | 0.1 | 3.96 | 0.51 | (m) | |
| bind8 | ~1 | 4 | 4 | 4.51 | -0.15 | -0.13 | 0.1 | 2.12 | 0.31 | (m) | |
| aind6 | ~1 | 2 | 2 | 4.42 | -0.13 | -0.11 | 0.1 | 2.82 | 0.39 | (m) | |
| aind8 | ~1 | 3 | 3 | 3.03 | -0.10 | -0.09 | 0.1 | 2.78 | 0.38 | (i) | |
| cind5 | ~1 | 2 | 2 | 2.75 | -0.14 | -0.15 | 0.1 | 1.42 | 0.22 | (i) | |
| bind5 | ~1 | 1 | 1 | 2.57 | 0.07 | 0.08 | 0.1 | 5.18 | 0.62 | (i) | |
| bind7 | ~1 | 4 | 4 | 2.55 | 0.11 | 0.10 | 0.1 | 1.99 | 0.29 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| vrt_ind_W1 | ~~ | vrt_ind_W1 | 1 | 1 | 6.79 | 0.37 | 1.00 | 0.1 | 0.49 | 0.11 | (m) |
| vrt_ind_W1 | ~~ | vrt_ind_W1 | 4 | 4 | 4.75 | -0.35 | -1.00 | 0.1 | 0.38 | 0.09 | (m) |
| aind5 | ~~ | aind5 | 3 | 3 | 3.53 | 0.10 | 0.75 | 0.1 | 3.80 | 0.50 | (i) |
All from the most constrained model (longitudinal and group constraints).
| item | aspfin_W1 | aspfin_W2 | aspfin_W3 | aspfin_W4 | aspfin_W1_std | aspfin_W2_std | aspfin_W3_std | aspfin_W4_std |
|---|---|---|---|---|---|---|---|---|
| aasp12 | 0.77 | 0.65 | ||||||
| aasp13 | 0.98 | 0.88 | ||||||
| aasp14 | 0.66 | 0.49 | ||||||
| aasp15 | 0.78 | 0.64 | ||||||
| aasp16 | 0.89 | 0.80 | ||||||
| basp12 | 0.77 | 0.64 | ||||||
| basp13 | 0.98 | 0.87 | ||||||
| basp14 | 0.66 | 0.48 | ||||||
| basp15 | 0.78 | 0.63 | ||||||
| basp16 | 0.89 | 0.79 | ||||||
| casp12 | 0.77 | 0.61 | ||||||
| casp13 | 0.98 | 0.86 | ||||||
| casp14 | 0.66 | 0.45 | ||||||
| casp15 | 0.78 | 0.60 | ||||||
| casp16 | 0.89 | 0.77 | ||||||
| dasp12 | 0.77 | 0.62 | ||||||
| dasp13 | 0.98 | 0.86 | ||||||
| dasp14 | 0.66 | 0.46 | ||||||
| dasp15 | 0.78 | 0.61 | ||||||
| dasp16 | 0.89 | 0.77 |
| item | bfa_mt_W1 | bfa_mt_W2 | bfa_mt_W3 | bfa_mt_W4 | bfa_mt_W1_std | bfa_mt_W2_std | bfa_mt_W3_std | bfa_mt_W4_std |
|---|---|---|---|---|---|---|---|---|
| abfas113 | -0.62 | -0.50 | ||||||
| abfas114 | -0.66 | -0.63 | ||||||
| abfas115 | -0.79 | -0.65 | ||||||
| abfas116 | 0.71 | 0.62 | ||||||
| abfas117 | 0.61 | 0.57 | ||||||
| abfas118 | 0.83 | 0.73 | ||||||
| bbfas113 | -0.62 | -0.47 | ||||||
| bbfas114 | -0.66 | -0.59 | ||||||
| bbfas115 | -0.79 | -0.61 | ||||||
| bbfas116 | 0.71 | 0.58 | ||||||
| bbfas117 | 0.61 | 0.54 | ||||||
| bbfas118 | 0.83 | 0.70 | ||||||
| cbfas113 | -0.62 | -0.49 | ||||||
| cbfas114 | -0.66 | -0.62 | ||||||
| cbfas115 | -0.79 | -0.64 | ||||||
| cbfas116 | 0.71 | 0.61 | ||||||
| cbfas117 | 0.61 | 0.56 | ||||||
| cbfas118 | 0.83 | 0.73 | ||||||
| dbfas113 | -0.62 | -0.46 | ||||||
| dbfas114 | -0.66 | -0.58 | ||||||
| dbfas115 | -0.79 | -0.61 | ||||||
| dbfas116 | 0.71 | 0.57 | ||||||
| dbfas117 | 0.61 | 0.53 | ||||||
| dbfas118 | 0.83 | 0.69 |
| item | hrz_col_W1 | hrz_col_W2 | hrz_col_W3 | hrz_col_W4 | hrz_col_W1_std | hrz_col_W2_std | hrz_col_W3_std | hrz_col_W4_std |
|---|---|---|---|---|---|---|---|---|
| aind9 | 0.66 | 0.67 | ||||||
| aind10 | 0.66 | 0.75 | ||||||
| aind11 | 0.49 | 0.45 | ||||||
| aind12 | 0.51 | 0.63 | ||||||
| bind9 | 0.66 | 0.61 | ||||||
| bind10 | 0.66 | 0.70 | ||||||
| bind11 | 0.49 | 0.40 | ||||||
| bind12 | 0.51 | 0.57 | ||||||
| cind9 | 0.66 | 0.61 | ||||||
| cind10 | 0.66 | 0.70 | ||||||
| cind11 | 0.49 | 0.40 | ||||||
| cind12 | 0.51 | 0.57 | ||||||
| dind9 | 0.66 | 0.61 | ||||||
| dind10 | 0.66 | 0.70 | ||||||
| dind11 | 0.49 | 0.40 | ||||||
| dind12 | 0.51 | 0.57 |
| item | hrz_ind_W1 | hrz_ind_W2 | hrz_ind_W3 | hrz_ind_W4 | hrz_ind_W1_std | hrz_ind_W2_std | hrz_ind_W3_std | hrz_ind_W4_std |
|---|---|---|---|---|---|---|---|---|
| aind1 | 0.51 | 0.63 | ||||||
| aind2 | 0.71 | 0.67 | ||||||
| aind3 | 0.39 | 0.36 | ||||||
| aind4 | 0.27 | 0.32 | ||||||
| bind1 | 0.51 | 0.58 | ||||||
| bind2 | 0.71 | 0.63 | ||||||
| bind3 | 0.39 | 0.32 | ||||||
| bind4 | 0.27 | 0.28 | ||||||
| cind1 | 0.51 | 0.61 | ||||||
| cind2 | 0.71 | 0.65 | ||||||
| cind3 | 0.39 | 0.34 | ||||||
| cind4 | 0.27 | 0.30 | ||||||
| dind1 | 0.51 | 0.58 | ||||||
| dind2 | 0.71 | 0.63 | ||||||
| dind3 | 0.39 | 0.32 | ||||||
| dind4 | 0.27 | 0.28 |
| item | mvi_W1 | mvi_W2 | mvi_W3 | mvi_W4 | mvi_W1_std | mvi_W2_std | mvi_W3_std | mvi_W4_std |
|---|---|---|---|---|---|---|---|---|
| aval7 | 0.90 | 0.53 | ||||||
| aval9 | 0.77 | 0.58 | ||||||
| aval11 | 0.87 | 0.53 | ||||||
| aval13 | 0.59 | 0.44 | ||||||
| aval15 | 0.84 | 0.53 | ||||||
| aval17 | 0.84 | 0.53 | ||||||
| aval18 | 0.97 | 0.51 | ||||||
| aval20 | 0.86 | 0.59 | ||||||
| aval21 | 0.71 | 0.53 | ||||||
| aval23 | 0.74 | 0.48 | ||||||
| aval8 | 0.74 | 0.38 | ||||||
| aval10 | 0.59 | 0.30 | ||||||
| aval12 | 0.42 | 0.21 | ||||||
| aval14 | 0.87 | 0.48 | ||||||
| aval16 | 0.82 | 0.48 | ||||||
| aval19 | 0.82 | 0.44 | ||||||
| aval22 | 0.83 | 0.43 | ||||||
| bval7 | 0.90 | 0.52 | ||||||
| bval9 | 0.77 | 0.57 | ||||||
| bval11 | 0.87 | 0.52 | ||||||
| bval13 | 0.59 | 0.42 | ||||||
| bval15 | 0.84 | 0.51 | ||||||
| bval17 | 0.84 | 0.52 | ||||||
| bval18 | 0.97 | 0.50 | ||||||
| bval20 | 0.86 | 0.57 | ||||||
| bval21 | 0.71 | 0.51 | ||||||
| bval23 | 0.74 | 0.46 | ||||||
| bval8 | 0.74 | 0.37 | ||||||
| bval10 | 0.59 | 0.29 | ||||||
| bval12 | 0.42 | 0.20 | ||||||
| bval14 | 0.87 | 0.47 | ||||||
| bval16 | 0.82 | 0.47 | ||||||
| bval19 | 0.82 | 0.43 | ||||||
| bval22 | 0.83 | 0.41 | ||||||
| cval7 | 0.90 | 0.53 | ||||||
| cval9 | 0.77 | 0.59 | ||||||
| cval11 | 0.87 | 0.54 | ||||||
| cval13 | 0.59 | 0.44 | ||||||
| cval15 | 0.84 | 0.53 | ||||||
| cval17 | 0.84 | 0.54 | ||||||
| cval18 | 0.97 | 0.52 | ||||||
| cval20 | 0.86 | 0.59 | ||||||
| cval21 | 0.71 | 0.53 | ||||||
| cval23 | 0.74 | 0.48 | ||||||
| cval8 | 0.74 | 0.38 | ||||||
| cval10 | 0.59 | 0.31 | ||||||
| cval12 | 0.42 | 0.21 | ||||||
| cval14 | 0.87 | 0.49 | ||||||
| cval16 | 0.82 | 0.49 | ||||||
| cval19 | 0.82 | 0.44 | ||||||
| cval22 | 0.83 | 0.43 | ||||||
| dval7 | 0.90 | 0.55 | ||||||
| dval9 | 0.77 | 0.60 | ||||||
| dval11 | 0.87 | 0.55 | ||||||
| dval13 | 0.59 | 0.46 | ||||||
| dval15 | 0.84 | 0.55 | ||||||
| dval17 | 0.84 | 0.55 | ||||||
| dval18 | 0.97 | 0.53 | ||||||
| dval20 | 0.86 | 0.61 | ||||||
| dval21 | 0.71 | 0.55 | ||||||
| dval23 | 0.74 | 0.50 | ||||||
| dval8 | 0.74 | 0.40 | ||||||
| dval10 | 0.59 | 0.32 | ||||||
| dval12 | 0.42 | 0.22 | ||||||
| dval14 | 0.87 | 0.50 | ||||||
| dval16 | 0.82 | 0.50 | ||||||
| dval19 | 0.82 | 0.46 | ||||||
| dval22 | 0.83 | 0.45 |
| item | usi_W1 | usi_W2 | usi_W3 | usi_W4 | usi_W1_std | usi_W2_std | usi_W3_std | usi_W4_std |
|---|---|---|---|---|---|---|---|---|
| ausi1 | 0.67 | 0.58 | ||||||
| ausi2 | -0.36 | -0.43 | ||||||
| ausi3 | -0.37 | -0.39 | ||||||
| ausi5 | 0.56 | 0.55 | ||||||
| ausi6 | -0.57 | -0.56 | ||||||
| ausi7 | 0.69 | 0.55 | ||||||
| busi1 | 0.67 | 0.60 | ||||||
| busi2 | -0.36 | -0.45 | ||||||
| busi3 | -0.37 | -0.42 | ||||||
| busi5 | 0.56 | 0.57 | ||||||
| busi6 | -0.57 | -0.58 | ||||||
| busi7 | 0.69 | 0.58 | ||||||
| cusi1 | 0.67 | 0.58 | ||||||
| cusi2 | -0.36 | -0.43 | ||||||
| cusi3 | -0.37 | -0.40 | ||||||
| cusi5 | 0.56 | 0.55 | ||||||
| cusi6 | -0.57 | -0.56 | ||||||
| cusi7 | 0.69 | 0.55 | ||||||
| dusi1 | 0.67 | 0.56 | ||||||
| dusi2 | -0.36 | -0.41 | ||||||
| dusi3 | -0.37 | -0.38 | ||||||
| dusi5 | 0.56 | 0.53 | ||||||
| dusi6 | -0.57 | -0.54 | ||||||
| dusi7 | 0.69 | 0.54 |
| item | vrt_col_W1 | vrt_col_W2 | vrt_col_W3 | vrt_col_W4 | vrt_col_W1_std | vrt_col_W2_std | vrt_col_W3_std | vrt_col_W4_std |
|---|---|---|---|---|---|---|---|---|
| aind13 | 0.74 | 0.68 | ||||||
| aind14 | 0.51 | 0.58 | ||||||
| aind15 | 0.82 | 0.75 | ||||||
| aind16 | 0.33 | 0.34 | ||||||
| bind13 | 0.74 | 0.69 | ||||||
| bind14 | 0.51 | 0.59 | ||||||
| bind15 | 0.82 | 0.76 | ||||||
| bind16 | 0.33 | 0.35 | ||||||
| cind13 | 0.74 | 0.69 | ||||||
| cind14 | 0.51 | 0.59 | ||||||
| cind15 | 0.82 | 0.76 | ||||||
| cind16 | 0.33 | 0.35 | ||||||
| dind13 | 0.74 | 0.71 | ||||||
| dind14 | 0.51 | 0.61 | ||||||
| dind15 | 0.82 | 0.78 | ||||||
| dind16 | 0.33 | 0.36 |
| item | vrt_ind_W1 | vrt_ind_W2 | vrt_ind_W3 | vrt_ind_W4 | vrt_ind_W1_std | vrt_ind_W2_std | vrt_ind_W3_std | vrt_ind_W4_std |
|---|---|---|---|---|---|---|---|---|
| aind5 | 0.46 | 0.50 | ||||||
| aind6 | 0.85 | 0.75 | ||||||
| aind7 | 0.67 | 0.56 | ||||||
| aind8 | 0.56 | 0.48 | ||||||
| bind5 | 0.46 | 0.46 | ||||||
| bind6 | 0.85 | 0.72 | ||||||
| bind7 | 0.67 | 0.53 | ||||||
| bind8 | 0.56 | 0.44 | ||||||
| cind5 | 0.46 | 0.48 | ||||||
| cind6 | 0.85 | 0.73 | ||||||
| cind7 | 0.67 | 0.55 | ||||||
| cind8 | 0.56 | 0.46 | ||||||
| dind5 | 0.46 | 0.41 | ||||||
| dind6 | 0.85 | 0.67 | ||||||
| dind7 | 0.67 | 0.47 | ||||||
| dind8 | 0.56 | 0.39 |
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 140 | 120 | 0.996 | 0.989 | 0.028 [0.000, 0.045] | |||||
| 2 | long_metric | 175 | 144 | -12.7 | -127.1 | 0.994 | -0.002 | 0.982 | -0.006 | 0.032 [0.007, 0.047] | |
| 3 | long_strong | 195 | 168 | -28.4 | -142.7 | 0.995 | 0.001 | 0.985 | 0.002 | 0.027 [0.000, 0.042] | |
| 4 | long_strict | 227 | 204 | -39.8 | -211.3 | 0.996 | 0.001 | 0.987 | 0.002 | -0.002 | 0.023 [0.000, 0.038] |
| 5 | metric | 236 | 213 | -8.5 | -51.4 | 0.996 | -0.000 | 0.987 | -0.000 | 0.004 | 0.023 [0.000, 0.038] |
| 6 | strong | 251 | 222 | -3.4 | -46.2 | 0.994 | -0.001 | 0.983 | -0.003 | -0.001 | 0.025 [0.000, 0.039] |
| 7 | strict | 263 | 231 | -6.5 | -49.4 | 0.994 | -0.000 | 0.982 | -0.001 | -0.005 | 0.025 [0.000, 0.039] |
Some improvement. Better overall fit, improved invariance, but still has \(\Delta\text{MFI}\) = .016 (versus .023 previously). Dropped asp14: You will be your own boss.; asp16: You will have a job that pays well.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 970 | 536 | 0.933 | 0.779 | 0.061 [0.055, 0.067] | |||||
| 2 | long_metric | 1033 | 584 | -32.4 | -261.2 | 0.931 | -0.002 | 0.772 | -0.007 | 0.060 [0.054, 0.065] | |
| 3 | long_strong | 1089 | 632 | -40.7 | -269.4 | 0.930 | -0.001 | 0.768 | -0.003 | 0.058 [0.052, 0.063] | |
| 4 | long_strict | 1171 | 692 | -37.6 | -323.5 | 0.926 | -0.003 | 0.759 | -0.010 | -0.020 | 0.057 [0.051, 0.062] |
| 5 | metric | 1183 | 707 | -18.5 | -90.0 | 0.927 | 0.001 | 0.760 | 0.002 | -0.012 | 0.056 [0.050, 0.061] |
| 6 | strong | 1216 | 722 | 3.7 | -67.8 | 0.924 | -0.003 | 0.752 | -0.008 | -0.016 | 0.056 [0.051, 0.062] |
| 7 | strict | 1253 | 737 | 6.3 | -65.2 | 0.921 | -0.003 | 0.743 | -0.009 | -0.016 | 0.057 [0.051, 0.062] |
Some improvement. Better overall fit, improved invariance, but still has \(\Delta\text{MFI}\) = .016 (versus >.024 previously). Also solved convergence problems. Dropped bfas113: I would be happier if I could afford to buy more things.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 140 | 120 | 0.994 | 0.989 | 0.028 [0.000, 0.045] | |||||
| 2 | long_metric | 178 | 144 | -9.6 | -124.0 | 0.990 | -0.004 | 0.980 | -0.008 | 0.033 [0.012, 0.048] | |
| 3 | long_strong | 232 | 168 | 5.6 | -108.7 | 0.982 | -0.008 | 0.964 | -0.017 | 0.042 [0.028, 0.054] | |
| 4 | long_strict | 278 | 204 | -26.2 | -197.7 | 0.979 | -0.003 | 0.958 | -0.005 | -0.030 | 0.041 [0.028, 0.052] |
| 5 | metric | 300 | 213 | 4.7 | -38.2 | 0.975 | -0.004 | 0.951 | -0.008 | -0.030 | 0.044 [0.031, 0.055] |
| 6 | strong | 368 | 222 | 49.1 | 6.2 | 0.959 | -0.016 | 0.919 | -0.031 | -0.044 | 0.055 [0.045, 0.065] |
| 7 | strict | 405 | 231 | 19.6 | -23.2 | 0.951 | -0.008 | 0.904 | -0.015 | -0.054 | 0.059 [0.049, 0.068] |
Some improvement. Better overall fit, improved invariance, but still has \(\Delta\text{MFI}\) = .032 (versus .056 previously). Dropped ind11: To me, pleasure is spending time with others.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 172 | 120 | 0.976 | 0.970 | 0.045 [0.029, 0.059] | |||||
| 2 | long_metric | 212 | 144 | -8.1 | -122.4 | 0.969 | -0.007 | 0.961 | -0.009 | 0.047 [0.033, 0.060] | |
| 3 | long_strong | 233 | 168 | -26.9 | -141.3 | 0.970 | 0.001 | 0.963 | 0.002 | 0.042 [0.028, 0.055] | |
| 4 | long_strict | 272 | 204 | -33.4 | -204.9 | 0.969 | -0.001 | 0.961 | -0.001 | -0.009 | 0.039 [0.026, 0.051] |
| 5 | metric | 287 | 213 | -2.9 | -45.8 | 0.966 | -0.003 | 0.958 | -0.003 | -0.003 | 0.040 [0.027, 0.052] |
| 6 | strong | 311 | 222 | 6.1 | -36.7 | 0.959 | -0.007 | 0.950 | -0.008 | -0.013 | 0.043 [0.031, 0.054] |
| 7 | strict | 323 | 231 | -6.5 | -49.4 | 0.958 | -0.001 | 0.948 | -0.001 | -0.013 | 0.043 [0.031, 0.054] |
About the same. Better overall fit. May not be necessary to drop items (but \(\Delta\text{MFI}\) is .12 from long strict to strict in both cases). Dropped ind1: I’d rather depend on myself than others.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 210 | 120 | 0.958 | 0.949 | 0.059 [0.045, 0.072] | |||||
| 2 | long_metric | 191 | 144 | -67.1 | -181.4 | 0.978 | 0.020 | 0.973 | 0.024 | 0.039 [0.022, 0.053] | |
| 3 | long_strong | 212 | 168 | -27.4 | -141.7 | 0.980 | 0.002 | 0.975 | 0.002 | 0.035 [0.017, 0.048] | |
| 4 | long_strict | 284 | 204 | 0.7 | -170.8 | 0.963 | -0.017 | 0.955 | -0.020 | 0.005 | 0.043 [0.030, 0.054] |
| 5 | metric | 270 | 213 | -32.9 | -75.8 | 0.974 | 0.011 | 0.968 | 0.013 | -0.005 | 0.035 [0.020, 0.047] |
| 6 | strong | 322 | 222 | 34.7 | -8.2 | 0.953 | -0.020 | 0.944 | -0.024 | -0.031 | 0.046 [0.034, 0.056] |
| 7 | strict | 331 | 231 | -9.7 | -52.6 | 0.954 | 0.000 | 0.944 | 0.000 | -0.010 | 0.045 [0.033, 0.055] |
Worse invariance, but better overall fit indices. Dropped usi1: The pleasures of the senses are the highest good.; usi2: People ought to be motivated by something beyond their own self-interest.; usi5: Worldly possessions are the greatest good and the highest value in life.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 162 | 120 | 0.989 | 0.976 | 0.040 [0.022, 0.055] | |||||
| 2 | long_metric | 180 | 144 | -29.8 | -144.2 | 0.991 | 0.001 | 0.979 | 0.003 | 0.034 [0.014, 0.049] | |
| 3 | long_strong | 208 | 168 | -20.1 | -134.5 | 0.990 | -0.001 | 0.977 | -0.002 | 0.033 [0.014, 0.047] | |
| 4 | long_strict | 254 | 204 | -25.5 | -197.0 | 0.987 | -0.003 | 0.971 | -0.006 | -0.005 | 0.034 [0.018, 0.046] |
| 5 | metric | 286 | 213 | 14.1 | -28.8 | 0.981 | -0.006 | 0.958 | -0.013 | -0.021 | 0.040 [0.027, 0.051] |
| 6 | strong | 320 | 222 | 15.5 | -27.4 | 0.975 | -0.006 | 0.945 | -0.013 | -0.032 | 0.045 [0.034, 0.056] |
| 7 | strict | 335 | 231 | -2.8 | -45.6 | 0.973 | -0.002 | 0.942 | -0.003 | -0.030 | 0.046 [0.034, 0.056] |
Some improvement. Still not perfect. Only three items. Very good fit indices. Dropped ind16: It is important to me that I respect the decisions made by my groups.
| Type | \(\chi^2\) | \(\text{Df}\) | \(\Delta\text{AIC}\) | \(\Delta\text{BIC}\) | \(\text{CFI}\) | \(\Delta\text{CFI}\) | \(\text{MFI}\) | \(\Delta\text{MFI}\) | \(\Delta_{1,4}\text{MFI}\) | \(\text{RMSEA}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | unconstrained | 135 | 120 | 0.996 | 0.991 | 0.024 [0.000, 0.043] | |||||
| 2 | long_metric | 168 | 144 | -15.0 | -129.4 | 0.993 | -0.003 | 0.986 | -0.005 | 0.028 [0.000, 0.044] | |
| 3 | long_strong | 192 | 168 | -23.4 | -137.7 | 0.993 | -0.000 | 0.986 | -0.000 | 0.026 [0.000, 0.042] | |
| 4 | long_strict | 230 | 204 | -33.9 | -205.4 | 0.992 | -0.001 | 0.985 | -0.001 | -0.007 | 0.024 [0.000, 0.039] |
| 5 | metric | 242 | 213 | -6.8 | -49.7 | 0.991 | -0.001 | 0.984 | -0.001 | -0.003 | 0.025 [0.000, 0.039] |
| 6 | strong | 263 | 222 | 3.7 | -39.1 | 0.988 | -0.004 | 0.976 | -0.007 | -0.010 | 0.029 [0.010, 0.042] |
| 7 | strict | 274 | 231 | -7.6 | -50.5 | 0.987 | -0.000 | 0.976 | -0.001 | -0.009 | 0.029 [0.010, 0.042] |
Better. Difference between strict and long_strict is ~< .01. Dropped ind8: When another person does better than I do, I get tense and aroused.
For some reason lavaan orders the groups like this:
Looking at issues with strict longitudinal invariance.
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| aspfin_W1 | =~ | aasp12 | 4 | 4 | 4.23 | -0.12 | -0.10 | 0.1 | 3.09 | 0.42 | (m) |
| aspfin_W3 | =~ | casp12 | 3 | 3 | 4.08 | 0.12 | 0.10 | 0.1 | 2.87 | 0.39 | (m) |
| aspfin_W4 | =~ | dasp15 | 1 | 1 | 2.80 | -0.08 | -0.07 | 0.1 | 4.27 | 0.54 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| aspfin_W1 | ~1 | 1 | 1 | 7.24 | 0.21 | 0.21 | 0.1 | 1.58 | 0.24 | (m) | |
| aspfin_W1 | ~1 | 4 | 4 | 3.50 | -0.17 | -0.17 | 0.1 | 1.23 | 0.20 | (i) | |
| aspfin_W1 | ~1 | 2 | 2 | 3.01 | -0.19 | -0.19 | 0.1 | 0.88 | 0.16 | (i) | |
| casp15 | ~1 | 4 | 4 | 2.82 | -0.11 | -0.10 | 0.1 | 2.18 | 0.31 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| casp12 | ~~ | casp12 | 2 | 2 | 4.86 | 0.16 | 0.51 | 0.1 | 1.92 | 0.28 | (m) |
| aspfin_W1 | ~~ | aspfin_W1 | 1 | 1 | 2.76 | 0.21 | 1.00 | 0.1 | 0.64 | 0.13 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| bfa_mt_W1 | =~ | abfas117 | 2 | 2 | 6.01 | -0.20 | -0.19 | 0.1 | 1.50 | 0.23 | (m) |
| bfa_mt_W1 | =~ | abfas116 | 2 | 2 | 4.15 | 0.17 | 0.15 | 0.1 | 1.45 | 0.23 | (m) |
| bfa_mt_W1 | =~ | abfas115 | 2 | 2 | 3.03 | 0.14 | 0.12 | 0.1 | 1.44 | 0.22 | (i) |
| bfa_mt_W2 | =~ | bbfas115 | 1 | 1 | 2.90 | 0.10 | 0.09 | 0.1 | 2.80 | 0.39 | (i) |
| bfa_mt_W4 | =~ | dbfas115 | 3 | 3 | 2.81 | -0.12 | -0.10 | 0.1 | 1.85 | 0.27 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| bfa_mt_W1 | ~1 | 1 | 1 | 10.49 | -0.26 | -0.26 | 0.1 | 1.57 | 0.24 | (m) | |
| bfa_mt_W1 | ~1 | 2 | 2 | 9.26 | 0.32 | 0.32 | 0.1 | 0.89 | 0.16 | (m) | |
| abfas118 | ~1 | 2 | 2 | 9.25 | 0.22 | 0.20 | 0.1 | 1.83 | 0.27 | (m) | |
| cbfas114 | ~1 | 1 | 1 | 6.52 | -0.12 | -0.11 | 0.1 | 4.41 | 0.56 | (m) | |
| dbfas114 | ~1 | 1 | 1 | 5.84 | 0.12 | 0.11 | 0.1 | 4.31 | 0.55 | (m) | |
| bfa_mt_W1 | ~1 | 4 | 4 | 5.59 | 0.21 | 0.21 | 0.1 | 1.22 | 0.20 | (m) | |
| dbfas118 | ~1 | 4 | 4 | 4.14 | -0.15 | -0.14 | 0.1 | 1.77 | 0.26 | (m) | |
| dbfas116 | ~1 | 1 | 1 | 4.14 | 0.12 | 0.10 | 0.1 | 2.91 | 0.40 | (m) | |
| abfas115 | ~1 | 3 | 3 | 3.81 | 0.11 | 0.09 | 0.1 | 2.90 | 0.40 | (i) | |
| bbfas114 | ~1 | 3 | 3 | 3.03 | 0.09 | 0.08 | 0.1 | 3.94 | 0.51 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| cbfas118 | ~~ | cbfas118 | 2 | 2 | 6.89 | 0.27 | 0.39 | 0.1 | 0.96 | 0.16 | (m) |
| dbfas118 | ~~ | dbfas118 | 3 | 3 | 6.56 | 0.19 | 0.46 | 0.1 | 1.74 | 0.26 | (m) |
| bbfas116 | ~~ | bbfas116 | 2 | 2 | 4.73 | 0.24 | 0.58 | 0.1 | 0.83 | 0.15 | (m) |
| cbfas118 | ~~ | cbfas118 | 3 | 3 | 3.36 | -0.14 | -0.44 | 0.1 | 1.76 | 0.26 | (i) |
| cbfas117 | ~~ | cbfas117 | 4 | 4 | 3.27 | 0.15 | 0.68 | 0.1 | 1.54 | 0.24 | (i) |
| bbfas116 | ~~ | bbfas116 | 3 | 3 | 3.02 | -0.12 | -0.60 | 0.1 | 2.09 | 0.30 | (i) |
| dbfas115 | ~~ | dbfas115 | 1 | 1 | 2.70 | -0.12 | -0.56 | 0.1 | 1.74 | 0.26 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| hrz_col_W1 | =~ | aind9 | 1 | 1 | 5.74 | 0.11 | 0.11 | 0.1 | 4.49 | 0.56 | (m) |
| hrz_col_W2 | =~ | bind10 | 1 | 1 | 3.92 | -0.09 | -0.10 | 0.1 | 4.73 | 0.59 | (m) |
| hrz_col_W1 | =~ | aind12 | 3 | 3 | 3.27 | -0.08 | -0.10 | 0.1 | 5.35 | 0.64 | (i) |
| hrz_col_W4 | =~ | dind9 | 1 | 1 | 2.84 | -0.09 | -0.09 | 0.1 | 3.71 | 0.49 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| hrz_col_W1 | ~1 | 1 | 1 | 29.98 | -0.45 | -0.45 | 0.1 | 1.47 | 0.23 | (m) | |
| hrz_col_W1 | ~1 | 2 | 2 | 20.94 | 0.50 | 0.50 | 0.1 | 0.83 | 0.15 | (m) | |
| aind9 | ~1 | 1 | 1 | 17.37 | -0.18 | -0.18 | 0.1 | 5.50 | 0.65 | (m) | |
| aind12 | ~1 | 2 | 2 | 6.79 | 0.14 | 0.17 | 0.1 | 3.55 | 0.47 | (m) | |
| bind9 | ~1 | 1 | 1 | 5.89 | -0.11 | -0.11 | 0.1 | 5.15 | 0.62 | (m) | |
| cind9 | ~1 | 2 | 2 | 5.82 | 0.13 | 0.15 | 0.1 | 3.42 | 0.46 | (m) | |
| aind10 | ~1 | 2 | 2 | 5.48 | 0.13 | 0.15 | 0.1 | 3.17 | 0.43 | (m) | |
| aind12 | ~1 | 4 | 4 | 4.98 | 0.09 | 0.12 | 0.1 | 5.57 | 0.66 | (m) | |
| bind10 | ~1 | 1 | 1 | 4.35 | 0.09 | 0.10 | 0.1 | 5.87 | 0.68 | (m) | |
| bind12 | ~1 | 3 | 3 | 4.07 | -0.09 | -0.11 | 0.1 | 4.69 | 0.58 | (m) | |
| dind12 | ~1 | 4 | 4 | 3.61 | -0.10 | -0.13 | 0.1 | 3.39 | 0.45 | (i) | |
| aind12 | ~1 | 3 | 3 | 3.60 | 0.07 | 0.09 | 0.1 | 6.57 | 0.73 | (i) | |
| cind10 | ~1 | 2 | 2 | 3.13 | -0.11 | -0.15 | 0.1 | 2.54 | 0.36 | (i) | |
| hrz_col_W1 | ~1 | 4 | 4 | 2.57 | 0.15 | 0.15 | 0.1 | 1.14 | 0.19 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| aind9 | ~~ | aind9 | 1 | 1 | 9.96 | 0.14 | 0.53 | 0.1 | 5.11 | 0.62 | (m) |
| hrz_col_W1 | ~~ | hrz_col_W1 | 4 | 4 | 9.60 | -0.47 | -1.00 | 0.1 | 0.43 | 0.10 | (m) |
| hrz_col_W1 | ~~ | hrz_col_W1 | 1 | 1 | 6.87 | 0.35 | 1.00 | 0.1 | 0.55 | 0.11 | (m) |
| aind10 | ~~ | aind10 | 2 | 2 | 5.02 | -0.11 | -0.41 | 0.1 | 4.03 | 0.52 | (m) |
| bind12 | ~~ | bind12 | 1 | 1 | 2.85 | 0.07 | 0.65 | 0.1 | 6.59 | 0.73 | (i) |
| aind12 | ~~ | aind12 | 4 | 4 | 2.67 | -0.06 | -0.64 | 0.1 | 8.10 | 0.81 | (nm) |
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: hrz_ind_W1 hrz_ind_W3 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| hrz_ind_W2 | =~ | bind2 | 1 | 1 | 2.71 | 0.14 | 0.12 | 0.1 | 1.45 | 0.23 | (i) |
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: hrz_ind_W1 hrz_ind_W3 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| hrz_ind_W1 | ~1 | 1 | 1 | 6.94 | 0.27 | 0.27 | 0.1 | 0.98 | 0.17 | (m) | |
| hrz_ind_W1 | ~1 | 4 | 4 | 4.34 | -0.24 | -0.24 | 0.1 | 0.76 | 0.14 | (m) | |
| cind4 | ~1 | 3 | 3 | 3.58 | -0.10 | -0.12 | 0.1 | 3.39 | 0.45 | (i) | |
| aind4 | ~1 | 1 | 1 | 3.38 | 0.08 | 0.09 | 0.1 | 5.67 | 0.66 | (i) | |
| dind4 | ~1 | 1 | 1 | 2.56 | -0.07 | -0.09 | 0.1 | 4.59 | 0.57 | (i) |
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: hrz_ind_W1 hrz_ind_W3 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| bind4 | ~~ | bind4 | 2 | 2 | 2.55 | 0.1 | 0.71 | 0.1 | 2.34 | 0.33 | (i) |
It’s not clear that we can trust the invariance tests for this scale.
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W3 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W3 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W2 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 4]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| usi_W1 | =~ | ausi3 | 4 | 4 | 5.7 | 0.17 | 0.18 | 0.1 | 1.93 | 0.28 | (m) |
| usi_W4 | =~ | dusi3 | 3 | 3 | 3.0 | 0.15 | 0.13 | 0.1 | 1.32 | 0.21 | (i) |
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W3 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W3 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W2 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 4]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| usi_W1 | ~1 | 1 | 1 | 18.80 | -0.43 | -0.43 | 0.1 | 1.01 | 0.17 | (m) | |
| usi_W1 | ~1 | 2 | 2 | 7.77 | 0.40 | 0.40 | 0.1 | 0.49 | 0.11 | (m) | |
| ausi7 | ~1 | 4 | 4 | 5.07 | -0.16 | -0.13 | 0.1 | 1.92 | 0.28 | (m) | |
| ausi7 | ~1 | 1 | 1 | 4.19 | 0.12 | 0.09 | 0.1 | 2.97 | 0.41 | (m) | |
| ausi3 | ~1 | 1 | 1 | 3.76 | -0.09 | -0.10 | 0.1 | 4.36 | 0.55 | (i) | |
| dusi7 | ~1 | 2 | 2 | 3.67 | -0.20 | -0.15 | 0.1 | 0.93 | 0.16 | (i) | |
| cusi7 | ~1 | 3 | 3 | 2.86 | 0.12 | 0.10 | 0.1 | 1.99 | 0.29 | (i) | |
| ausi3 | ~1 | 4 | 4 | 2.64 | -0.10 | -0.10 | 0.1 | 2.74 | 0.38 | (i) | |
| busi7 | ~1 | 4 | 4 | 2.62 | -0.13 | -0.11 | 0.1 | 1.50 | 0.23 | (i) |
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W3 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W3 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W2 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W1 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W2 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
## variables involved are: usi_W3 usi_W4 [in block 4]
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| usi_W3 | ~~ | usi_W3 | 4 | 4 | 4.81 | -0.29 | -1.00 | 0.1 | 0.58 | 0.12 | (m) |
| usi_W1 | ~~ | usi_W1 | 2 | 2 | 3.95 | 0.90 | 1.00 | 0.1 | 0.05 | 0.06 | (m) |
| usi_W1 | ~~ | usi_W1 | 4 | 4 | 3.84 | -0.34 | -1.00 | 0.1 | 0.33 | 0.09 | (i) |
| ausi7 | ~~ | ausi7 | 2 | 2 | 3.26 | 0.25 | 0.82 | 0.1 | 0.51 | 0.11 | (i) |
| busi6 | ~~ | busi6 | 4 | 4 | 3.15 | -0.17 | -0.57 | 0.1 | 1.03 | 0.17 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| vrt_col_W3 | =~ | cind14 | 1 | 1 | 6.68 | 0.11 | 0.14 | 0.1 | 5.37 | 0.64 | (m) |
| vrt_col_W3 | =~ | cind14 | 4 | 4 | 6.00 | -0.15 | -0.17 | 0.1 | 2.82 | 0.39 | (m) |
| vrt_col_W1 | =~ | aind14 | 4 | 4 | 4.63 | -0.10 | -0.11 | 0.1 | 4.91 | 0.60 | (m) |
| vrt_col_W1 | =~ | aind15 | 2 | 2 | 3.12 | 0.13 | 0.12 | 0.1 | 1.77 | 0.26 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| cind14 | ~1 | 1 | 1 | 9.14 | -0.15 | -0.16 | 0.1 | 4.24 | 0.54 | (m) | |
| aind13 | ~1 | 1 | 1 | 7.84 | -0.13 | -0.12 | 0.1 | 4.66 | 0.58 | (m) | |
| aind15 | ~1 | 1 | 1 | 4.11 | 0.10 | 0.09 | 0.1 | 4.44 | 0.56 | (m) | |
| cind13 | ~1 | 1 | 1 | 4.09 | 0.11 | 0.09 | 0.1 | 3.67 | 0.48 | (m) | |
| cind15 | ~1 | 4 | 4 | 3.86 | -0.12 | -0.11 | 0.1 | 2.70 | 0.38 | (m) | |
| cind13 | ~1 | 2 | 2 | 2.88 | -0.14 | -0.12 | 0.1 | 1.58 | 0.24 | (i) | |
| vrt_col_W1 | ~1 | 1 | 1 | 2.79 | -0.14 | -0.14 | 0.1 | 1.45 | 0.23 | (i) | |
| cind14 | ~1 | 2 | 2 | 2.65 | 0.08 | 0.09 | 0.1 | 4.23 | 0.54 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| cind14 | ~~ | cind14 | 1 | 1 | 13.79 | 0.18 | 0.59 | 0.1 | 4.21 | 0.54 | (m) |
| dind15 | ~~ | dind15 | 1 | 1 | 2.90 | -0.10 | -0.35 | 0.1 | 2.91 | 0.40 | (i) |
| aind15 | ~~ | aind15 | 3 | 3 | 2.90 | 0.10 | 0.42 | 0.1 | 2.87 | 0.40 | (i) |
| aind13 | ~~ | aind13 | 1 | 1 | 2.61 | 0.08 | 0.53 | 0.1 | 3.64 | 0.48 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| vrt_ind_W4 | =~ | dind7 | 4 | 4 | 3.5 | 0.19 | 0.13 | 0.1 | 1.02 | 0.17 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| vrt_ind_W1 | ~1 | 2 | 2 | 7.79 | -0.32 | -0.32 | 0.1 | 0.76 | 0.14 | (m) | |
| aind6 | ~1 | 2 | 2 | 4.71 | -0.13 | -0.12 | 0.1 | 2.74 | 0.38 | (m) | |
| vrt_ind_W1 | ~1 | 1 | 1 | 4.30 | 0.18 | 0.18 | 0.1 | 1.34 | 0.21 | (m) | |
| bind5 | ~1 | 1 | 1 | 3.34 | 0.08 | 0.09 | 0.1 | 5.15 | 0.62 | (i) | |
| cind5 | ~1 | 2 | 2 | 3.11 | -0.15 | -0.16 | 0.1 | 1.40 | 0.22 | (i) |
| lhs | op | rhs | block | group | mi | epc | sepc.all | delta | ncp | power | decision |
|---|---|---|---|---|---|---|---|---|---|---|---|
| vrt_ind_W1 | ~~ | vrt_ind_W1 | 1 | 1 | 3.55 | 0.28 | 1.00 | 0.1 | 0.46 | 0.10 | (i) |
| vrt_ind_W1 | ~~ | vrt_ind_W1 | 4 | 4 | 3.17 | -0.30 | -1.00 | 0.1 | 0.35 | 0.09 | (i) |
| aind5 | ~~ | aind5 | 3 | 3 | 2.93 | 0.09 | 0.77 | 0.1 | 3.73 | 0.49 | (i) |